According to the statement the 7th term of the geometric sequence with first term 625 and common ratio -1/5 is 0.04.
The geometric sequence given by a₁ = 625 and a₂ = -125 will be given by the formula:an = a₁rⁿ⁻¹ where r is the common ratio. To find r, we can use the formula for the common ratio: r = a₂ / a₁. Thus, r = (-125) / 625 = -1 / 5.Hence, the formula of the sequence is an = 625 (-1 / 5)ⁿ⁻¹.To find the 7th term of this sequence, we can substitute n = 7 into the formula above: a₇ = 625 (-1 / 5)⁷⁻¹. In mathematics, a sequence is a series of numbers or other things in which each item is referred to as a term.
A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a fixed constant. The formula for the nth term of a geometric sequence is an = a₁rⁿ⁻¹, where a₁ is the first term, r is the common ratio, and n is the number of the term.
The problem provides us with the first two terms of the geometric sequence, a₁ = 625 and a₂ = -125. To find the common ratio, we can use the formula: r = a₂ / a₁. In this case, r = (-125) / 625 = -1 / 5.Using the formula an = a₁rⁿ⁻¹, we can find any term in the sequence. In this case, we want to find the 7th term, so we plug in n = 7 into the formula:an = 625 (-1 / 5)⁷⁻¹ = 625 (-1 / 5)⁶ = 0.04.
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a hair stylist makes $44 each day that she works and makes approximately $16 in tips for each hair cut that she gives. if she wants to make at least $108 in one day, at least how many hair cuts does she need to give?
The hairstylist needs to give at least 4 haircuts to make at least $108 in one day.
We know that the hairstylist wants to make at least $108 in one day. Therefore, we can set up an equation:
Total income >= $108
$44 + $16x >= $108
Subtracting $44 from both sides, we get:
$16x >= $64
Dividing both sides by $16, we get:
x >= 4
So the hair stylist needs to give at least 4 haircuts to make at least $108 in one day.
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Simplify the rational
Answer:
x+8 / x-4
Step-by-step explanation:
Factor the top and bottom (numerator and denominator).
Simplify (cancel what's the same on top and bottom)
See image.
What is the answer to this
-5 + 7
An electron (charge−1.6× 10−19 c) moves on a path perpendicular to the direction of a uniform electric field of strength 2.0 n/c. how much work is done on the electron as it moves 14.0 cm?
when converting a rectangular equation into polar form or converting polar equations into rectangular form, what are the conversion equations you can use? quixlet
Rectangular coordinates use the x and y axes, while polar coordinates use the radius and angle. By converting between these coordinate systems, we can gain new insights into the same equation and solve problems using different methods.
When converting rectangular equations to polar form, we can use the following conversion equations:
1. r^2 = x^2 + y^2 (this is the equation for the radius in terms of x and y)
2. tanθ = y/x (this is the equation for the angle θ in terms of x and y)
Using these equations, we can convert any rectangular equation (in terms of x and y) to its equivalent polar form (in terms of r and θ).
On the other hand, when converting polar equations to rectangular form, we can use the following conversion equations:
1. x = r*cos(θ) (this is the equation for x in terms of r and θ)
2. y = r*sin(θ) (this is the equation for y in terms of r and θ)
Using these equations, we can convert any polar equation (in terms of r and θ) to its equivalent rectangular form (in terms of x and y).
It's important to note that when converting equations between rectangular and polar forms, we're essentially changing the coordinate system used to describe the equation.
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What type of model does the data suggest?
х
0
1
2
3
4
y
2.5
5
10
20
40
O
A.
constant
O
B. exponential
C. linear
O
D. quadratic
Answer:
D HOPE THIS HELPS YOU!!
ANSWER IS D
Step-by-step explanation:
The population of rabbits on an island is growing exponentially. In the year 2000, the population of rabbits was 950, and by 2003 the population had grown to 1000. Predict the population of rabbits in the year 2013, to the nearest whole number.
The population of rabbits in the year 2013 is 1186.
How to predict the population of rabbits in the year 2013?
To predict the population of rabbits in the year 2013, we can use exponential growth. The formula for exponential growth is:
P = P₀ * e^(rt)
where:
P = final population
P₀ = initial population (950)
r = the growth rate (we need to find this)
t = time elapsed (13 years)
We can use the data from 2003 to find the growth rate:
1000 = 950 * e^(r * 3)
1000 = 950 * e^(3r)
1000/950 = e^(3r)
ln (1000/950) = 3r
r = (ln(1000 / 950)) / 3
r = 0.0171
Now that we have the growth rate, we can use it to find the population in 2013:
P = 950 * e^(0.0171 * 13)
P = 1186
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write an equivalent expression to 2x+3 + 5x +6 by combining like trems.
When a job asks you; How many years of Basic Math experience do you have?
you put how many years you've been in school, right? do you include preschool? y or n?
Answer:
All the Years since First Grade
No, you would not include Preschool
Step-by-step explanation:
Technically, for this question, you would put the number of years since you began learning basic math. For the vast majority of children, they begin learning Basic Math such as adding and subtracting whole numbers in First Grade. Therefore, you would include all of the years since First Grade. Preschool usually teaches children about numbers and how to count, as well as develop their social skills. Preschool does not teach basic math because the children are just learning about numbers.
Mrs. Corazza paid $38.64 to fill up 12 gallons of gasoline in her car. What is the price for 1 gallon of gasoline?
A television that costs $500 is marked up 250%. What
is the new price of the television?
Cost - 500
Marked Up - 250
Margin - 71.4286
MxCxMA= $1,750
This may seem confusing, but its $1,750 for the new price, and the equation is:
M= Marked
C= Cost
MA= Margin
The new price of the television is $1750.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A television that costs $500 is marked up 250%.
So, the new price is
= 500 + 250% of 500
= 500 + 250/100 x 500
= 500 + 1250
= $1750
Hence, the new price of the television is $1750.
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Circle q was transformed wo create circle which rule best describes the transformation that was apphed to q to create circle q'?
The rule that best describes the transformation that was applied to circle q to create circle q' is a dilation.
A dilation is a transformation that stretches or shrinks a figure by a certain scale factor, while preserving its shape. In this case, circle q was transformed into circle q' by either stretching or shrinking it, resulting in a circle that is either larger or smaller than the original circle. Since the shape of the circle remained the same, we can conclude that a dilation was the transformation that was applied.
To fully understand the transformation that was applied to circle q, we need to look at the properties of dilations. A dilation is a type of transformation that changes the size of a figure, but not its shape. It is performed by multiplying the coordinates of each point by a scale factor, which can be greater than 1 to stretch the figure, or less than 1 to shrink it. To determine if a dilation was applied to circle q, we can compare its properties to those of circle q'. First, we can look at the radii of the two circles. If circle q' is larger or smaller than circle q by a certain factor, this would indicate that a dilation was used. We can also examine the center of dilation, which is the point around which the figure is stretched or shrunk. If the center of circle q' is the same as that of circle q, this would suggest that a dilation was performed.
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Sara’s mother is now four times as old as Sara. In five years, she will be three times as old as Sara. What are their ages now?
Answer:
Sara's mother age : 40 years
Sara's age : 10 years
Step-by-step explanation:
Let Sara's mother age be x
and Sara age be y
Given , Sara's mother is now four time as old as Sara
• x = 4y ...1
also, in five years , she will be three times as old as Sara
In five years , Sara's mother age :- ( x + 5 )
Sara age :- ( y + 5 )
according to the question,
x + 5 = 3 ( y + 5 )
x + 5 = 3y + 15
x - 3y = 10 ... 2
putting value of x from 1 into 2
4y - 3y = 10
y = 10
putting y value in 1
x = 4y = 4 ( 10 ) = 40
So, Sara's mother age is 40years
and Sara's age is 10years .
⚠️‼️ HELP PLEASE GIVING POINTS !!
Answer:
m∠QPR = 25°.
Step-by-step explanation:
If m∠QPR = 9x + 16°, substitute in 1 for 'x':. 9(1) + 16 = 9 + 16 = 25°
The function f(t)=16t2 represents the distance (in feet) a dropped object falls in t seconds. the function g(t)=s0 represents the initial height (in feet) of the object. a penny is dropped off of a building at a height of 256 feet. after how many seconds does the penny hit the ground?
The coin purse hit the ground in 3 seconds.
Given :
\($\mathrm{f}(\mathrm{t})=16 \mathrm{t}^2$\) ----- (represent the distance(in feet) a dropped object falls in t seconds)
\($\mathrm{g}(\mathrm{t})=\mathrm{s}_0=144 \mathrm{ft}$\) ------ (represent the initial height (in feet) of the coin purse)
The function that represents the distance a dropped coin purse falls in t seconds,
\($f(t)=144-16 t^2$\)
When the coin purse touches the ground,
\($f(t)=0$\)
\($0=144-16 t^2$\)
\($t^2=\frac{144}{16}=9$\)
t = +3 and t = -3
So we take positive t.
Therefore, the coin purse hit the ground in 3 seconds.
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f(x) = 2x + 3
g(x) = x
(a) Find fg(6).
(b) Solve the equation gf(x) = 100.
Answer:
a) 15
b) 97/2
Step-by-step explanation:
a) f(g(6))
g(6) = 6
2(6)+3
12 + 3
15
b) gf(x) = 10
2x+3
2x+3 = 100
2x = 97
x = 97/2
In a café, drinks are priced according to what size they are.
The table shows the different sizes and costs.
Size of drink
Extra Small
Cost
£1.00
£1.50
£2.00
£2.50
£3.00
Small
Medium
Large
Extra Large
a) Gavin pays for one extra small and three large drinks.
Altogether, how much did they cost?
b) Lian pays for one small, one medium and one extra large drink.
She pays with a £10 note.
How much change should she get?
Answer:
for A. Gavin would pay 10. because 1.00 + 3.00 + 3.00 + 3.00 is 10.
and for B. 1.50 + 2.00 + 3.00 = 6.50. so lian would get 3.50 change back.
3) Find f(x) given that f'(x) = 10x4 - 12x³ + 8e-4x + 7 and f(0) = -9. {8 pts}
Answer:
Find f(x) given that f'(x) = 10x4 - 12x³ + 8e-4x + 7 and f(0) = -9. {8 pts}
Step-by-step explanation:
Suppose that $696 is invested at 9.19% interest compounded quarterly. How much is in the account after 12 years? Round your answer to the nearest cent; do not enter the $ sign.
To find f(x), we need to integrate f'(x) with respect to x. The antiderivative of 10x^4 - 12x^3 is (2x^5 - 3x^4) + C, where C is an arbitrary constant of integration.
The antiderivative of 8e^(-4x) is -2e^(-4x) + K, where K is another constant of integration.
Therefore, the general solution for f(x) is:
f(x) = 2x^5 - 3x^4 - 2e^(-4x) + C
To solve for the constant C, we use the initial condition that f(0) = -9:
f(0) = 2(0)^5 - 3(0)^4 - 2e^(-4(0)) + C = -9
Simplifying this equation gives:
-2 + C = -9
C = -7
Therefore, the specific solution for f(x) is:
f(x) = 2x^5 - 3x^4 - 2e^(-4x) - 7
So, f(x) = 2x^5 - 3x^4 - 2e^(-4x) - 7 and f(0) = -9.
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Part a: Which relationship describes <1 and <2?
Part b: What is the value of x?
Part c: What is the m22?
Answer:
x = 8
Step-by-step explanation:
Part a: <1 and <2 are alternate exterior angles because line horizontal lines are parallel
Part b: the value of x can be calculated with the following equation
7x + 15 = 10x - 9 because alternate angles has same measure
15 + 9 = 10x - 7x
24 = 3x divide both sides by 3
8 = x
Is 1/5 greater than 0.2
Answer:
Yes and No
Step-by-step explanation:
It is the same value
1/5 is the same value as 0.2
Answer:
No thry are equal
Step-by-step explanation:
1/5=20/100
0.2= 0.20 or 20/100
I really need help with this
Answer:
I don't have a grid with me but look at it this way. if you look at the first set of points look at where they are starting. and. then look at the second set of points. see if the points plotted bend over the x axis or the y axis:)
In an LCR-circuit, the resistor (R) of 20Ω, inductance (L) of 0.2H, and the capacitor (C) of 2×10 −3
are in a series combination with the electromotive force which is given by the function E(t)=100cos(20t)V. Provided the condition that the current and the charge are zero at initially. Find the current at any time (t>0) with the help of Laplace transform.
In an LCR-circuit, the resistor (R) of 20Ω, inductance (L) of 0.2H, and the capacitor (C) of 2×10 −3
are in a series combination with the electromotive force which is given by the function E(t)=100cos(20t)V. Provided the condition that the current and the charge are zero at initially. Find the current at any time (t>0) with the help of Laplace transform.
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3. Estimate the subjective probability of each event and provide a rationale for your decision. a) All classes next week will be cancelled. b) At least one severe snow storm will occur in your area ne
Subjective probability is an individual’s personal estimate of the likelihood of an event occurring. a) If the weather forecast predicts mild weather conditions, the probability of this event occurring will be low. b) Depending on the climate of the region, the probability of a severe snowstorm happening varies.
a) All classes next week will be canceled: The subjective probability of this event depends on the weather forecast of the area. If the weather forecast predicts heavy snowfall, then the probability of all classes being canceled next week will be high. Hence, we cannot estimate the exact probability of this event happening, but we can predict the probability based on the weather forecast.
b) At least one severe snowstorm will occur in your area: In this case, the probability of the event happening is moderate to high. If the region is known for heavy snowfall, then the probability of this event occurring is high. If the region is not known for snowfall or is prone to mild snowfall, then the probability will be low. However, in most cases, the probability of a severe snowstorm occurring is moderate to high, especially during winter.
The given question is incomplete, the complete question is "Estimate the subjective probability of each event and provide a rationale for your decision. a) All classes next week will be canceled. b) At least one severe snowstorm will occur in your area next winter"
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Select the following correlation that demonstrates the WEAKEST correlation between two variables.
a) +.20
b) - 50
c) +.75 d
) - 76
The correlation that demonstrates the weakest correlation between two variables is option a) +.20.
Among the given options, the correlation that demonstrates the weakest correlation between two variables is option b) -50.
In correlation coefficients, the value ranges from -1 to +1, where -1 represents a perfect negative correlation, +1 represents a perfect positive correlation, and 0 represents no correlation or a very weak correlation.
Let's analyze the options provided:
a) +.20:
This indicates a positive correlation, but the value is relatively small (0.20).
It suggests a weak positive relationship between the variables.
b) -50:
This option appears to be a typographical error since the correlation coefficient cannot be negative 50.
Assuming it is meant to be -0.50, this indicates a moderate negative correlation.
c) +.75:
This option represents a strong positive correlation.
With a coefficient of 0.75, it suggests a relatively strong positive relationship between the variables.
d) -76: Similar to option b, this value appears to be a typographical error. A correlation coefficient cannot exceed the range of -1 to +1.
Assuming it is meant to be -0.76, this indicates a strong negative correlation.
Comparing the given options, the weakest correlation is option b) -50, assuming it was intended to be -0.50. A correlation coefficient of -0.50 represents a moderate negative correlation, which is weaker than the other options but still indicates some relationship between the variables.
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The length and width of a rectangle are consecutive integers. The area of the rectangle is 380 square meters. Find the length and width of the rectangle.
Answer:
19x20
Step-by-step explanation:
The area of a rectangle is given by the formula A = l * w, where l is the length and w is the width of the rectangle. In this case, we are given that the area of the rectangle is 380 square meters and that the length and width of the rectangle are consecutive integers.
We can use this information to create a system of equations to solve for the length and width of the rectangle. Let l be the length of the rectangle and w be the width of the rectangle. Since the length and width of the rectangle are consecutive integers, we have:
l = w + 1
Substituting this equation into the formula for the area of the rectangle, we get:
A = l * w
= (w + 1) * w
= w² + w
Since the area of the rectangle is given as 380 square meters, we can set this equation equal to 380 and solve for w:
w² + w = 380
To solve for w, we can use the quadratic formula, which is given by:
x = (-b ± √(b² - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation, and x is the solution. Substituting the values of a, b, and c into the formula and simplifying, we get:
w = (-1 ± √(1² - 4(1)(380))) / (2(1))
= (-1 ± √(-1519)) / 2
Since the length and width of the rectangle must be positive integers, we can ignore the negative solution and only consider the positive solution. Therefore, the width of the rectangle is 19.
To find the length of the rectangle, we can use the equation l = w + 1 that we derived earlier. Substituting the value of w into this equation, we get:
l = w + 1
= 19 + 1
= 20
Therefore, the length of the rectangle is 20 and the width of the rectangle is 19. The dimensions of the rectangle are 20 x 19.
select the correct answer. which point is a point where the graph of y = (x - 5)(X^2 - 7x + 12) Crosses the x axis
The graph of y = (x - 5)(X² - 7x + 12) Crosses the x axis at point ( 3,0), (4,0) and (5,0).
What is x-axis?Both the x-axis and the y-axis are number lines, but the x-axis is horizontal. The coordinate plane is created when these two axes come together perpendicularly. The ordinate and abscissa are other names for the ordinate and x, respectively, in a graph.
Given : y = (x - 5)(X² - 7x + 12)
If the given crosses the x-axis, then the value of y will be 0 at x-axis.
So, we have y=0 when it crosses x-axis.
Now, putting y=0 in the given equation,
we get, (x - 5)(X² - 7x + 12) = 0
Case 1 : x-5 = 0
x = 5
Case 2 : X^2 - 7x + 12 = 0
x² -3x - 4x + 12 = 0
x (x-3) - 4 (x-3) = 0
(x-3) (x-4) = 0
x = 3 and 4
So, We get x = 3,4 and 5.
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B = 4x + 30 C = 2/3 * x + 20 A = x + 30
Anyone know the answer to this?
Answer:
all the ways to answer
Step-by-step explanation:
B:
Factor:
2(2x+15)
Evaluate:
4x+30
C:
Factor:
2(x+30)/3
Evaluate:
2(x+30)/3
A:
DIFFERENTIATE W.R.T. X:
1
Evaluate:
x+30
hope that helps.
if correct please mark as brainliest
thank you
HAVE A NICE DAY
19NBoli
Use a formula to find the surface area of the figure. 13 in. T I ***** 11 in drawing not to scale 30 in. O 287 in. 2 858 in. O 574 in.
ANSWER:
The surface area of the figure is 574 in^2
STEP-BY-STEP EXPLANATION:
We have that the surface area of a rectangular prism is given by the following formula
\(\begin{gathered} A=2\cdot l\cdot w+2\cdot l\cdot h+2\cdot w\cdot h \\ \text{where l is the length, w is the width and h is the height} \end{gathered}\)replacing:
\(\begin{gathered} A=2\cdot11\cdot6+2\cdot11\cdot13+2\cdot6\cdot13 \\ A=132+286+156 \\ A=574 \end{gathered}\)10. The sum of the digits of a two digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27 . find the number
Answer:
Step-by-step explanation:
Let "ab" represent the digits of the number. The value of "ab" is 10a+b.
a+b = 7
The value of "ba" is 10b+a
(10b+a) - (10a+b) = 9b-9a = 27
b-a = 3
a+b = 7
b-a = 3
------------
2b = 10
b = 5
a = 2
The number is 25.
help i cant solve this
Answer:
\(\huge\boxed{\sf 44\ units}\)
Step-by-step explanation:
Perimeter:Sum of all sides of a figure is known as perimeter of that figure.Solution:
So,
Perimeter of this figure:= 3 + 8 + 3 + 6 + 5 + 6 (again) + 4 + 5 + 4
= 44 units\(\rule[225]{225}{2}\)
Answer:
8-4=4
therefore 6+4=10
then perimeter =2(5)+10+6+2(3)+8+4=44units